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Competency in Focus: Divisibility This problem from American Mathematics contest (AMC 8, 2017) is based on the concept of divisibility .

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Next understand the problem

Let \(Z\) be a 6-digit positive integer, such as 247247, whose first three digits are the same as its last three digits taken in the same order. Which of the following numbers must also be a factor of \(Z\)? \((A)11\qquad(B)19\qquad(A)101\qquad(A)111\qquad(A)1111\)
Source of the problem
American Mathematical Contest 2017, AMC 8  Problem 7
Key Competency
Difficulty Level
Suggested Book

Start with hints 

Do you really need a hint? Try it first!
Take \(Z\) as \(\overline{\rm ABCABC}\).
Calculate the alternating sum of the digits. i.e., \(A-B+C-A+B-C=0\) then it is dibisible by \(11\)

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